mirror of
https://github.com/bolero-MURAKAMI/Sprout
synced 2024-11-12 21:09:01 +00:00
60 lines
2.5 KiB
C++
60 lines
2.5 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2019 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_COMPLEX_TANH_HPP
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#define SPROUT_COMPLEX_TANH_HPP
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/math/isnan.hpp>
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#include <sprout/math/isinf.hpp>
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#include <sprout/math/sin.hpp>
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#include <sprout/math/copysign.hpp>
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#include <sprout/complex/complex.hpp>
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#include <sprout/complex/arithmetic_operators.hpp>
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#include <sprout/complex/cosh.hpp>
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#include <sprout/complex/sinh.hpp>
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namespace sprout {
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//
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// tanh
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//
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// G.6.2.6 The ctanh functions
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// ctanh(conj(z)) = conj(ctanh(z))and ctanh is odd.
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// ctanh(+0 + i0) returns +0 + i0.
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// ctanh(x + i<>‡) returns NaN + iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
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// ctanh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
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// ctanh(+<2B>‡+ iy) returns 1 + i0 sin(2y), for positive-signed finite y.
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// ctanh(+<2B>‡+ i<>‡) returns 1 <20>} i0 (where the sign of the imaginary part of the result is unspecified).
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// ctanh(+<2B>‡+ iNaN) returns 1 <20>} i0 (where the sign of the imaginary part of the result is unspecified).
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// ctanh(NaN + i0) returns NaN + i0.
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// ctanh(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for all nonzero numbers y.
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// ctanh(NaN + iNaN) returns NaN + iNaN.
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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tanh(sprout::complex<T> const& x) {
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typedef sprout::complex<T> type;
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return sprout::math::isnan(x.real())
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? sprout::math::isnan(x.imag()) ? x
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: x.imag() == 0 ? x
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: type(x.real(), x.real())
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: sprout::math::isnan(x.imag())
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? sprout::math::isinf(x.real()) ? type(T(1), T(0))
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: type(x.imag(), x.imag())
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: sprout::math::isinf(x.real())
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? sprout::math::isinf(x.imag()) ? type(T(1), T(0))
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: type(T(1), T(0) * sprout::math::sin(T(2) * x.imag()))
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: sprout::math::isinf(x.imag())
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? type(-sprout::numeric_limits<T>::quiet_NaN(), -sprout::numeric_limits<T>::quiet_NaN())
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: x.real() == 0 && x.imag() == 0 ? x
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: sprout::sinh(x) / sprout::cosh(x)
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_TANH_HPP
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